Earth Resources Laboratory :: Abstracts

An Integrated Seismic and Well Log Analysis for the Estimation of Reservoir Properties

Muhammed M. Saggaf

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on April 11, 2000 in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Abstract

We present an integrated approach for characterizing the reservoir and estimating its properties both at the well locations and in the inter-well regions. Such an approach can be an invaluable tool for attaining a detailed, consistent, and complete characterization of the reservoir, as not only does it incorporate all major sources of information that shape our understanding of the reservoir, including core descriptions, well logs, seismic data, and a prior knowledge of the geological setting of the region, but also it develops means for utilizing these sources of information in a unified manner that gives rise to a coherent framework for relating these sources of information to yield an integrated reservoir model. We analyze the different components of this approach, develop methodologies for improving the prediction accuracy of each, and link the mechanisms across these components to achieve an accurate and consistent characterization of the reservoir. The issues we tackle in this thesis can be broadly divided into four categories: enhancement of the seismic resolution, estimation of the reservoir properties at the well locations, characterizing in the inter-well regions, and pre-processing the data to remedy any incompleteness or inconsistency.

The first component of the approach we present in this thesis is concerned with enhancing the resolution of the seismic data by generalizing the conventional deconvolution method to utilize proper stochastic modeling of the underlying reflection coefficients of the earth. One of the fundamental assumptions of conventional deconvolution methods is that reflection coefficients follow the white noise model. However, analysis of well logs in various regions of the world observed that in the majority of cases reflectivity tends to depart from the white noise behavior. The assumption of white noise leads to a conventional deconvolution operator that can recover only the white component of reflectivity, thus yielding a distorted representation of the desired output. Various alternative processes have been suggested to model reflection coefficients. We examine some of these processes, apply them, contrast their stochastic properties, and critique their use for modeling reflectivity. These processes include ARMA, scaling Gaussian noise, fractional Brownian motion, fractional Gaussian noise, and fractionally integrated noise. We then present a consistent framework to generalize the conventional deconvolution procedure to handle reflection coefficients that do not follow the white noise model. This framework represents a unified approach to the problem of deconvolving signals of non-white reflectivity, and describes how higher-order solutions to the deconvolution problem can be realized. We test generalized filters based on the various stochastic models and analyze their output. Since these models approximate the stochastic properties of reflection coefficients to a much better degree than white noise, they yield generalize deconvolution filters that deliver a significant improvement on the accuracy of seismic deconvolution over the conventional operator.

In the second component, we aim to provide an accurate and consistent characterization of the reservoir properties at the well locations, since the description of the reservoir invariably relies on its sampling at these locations. We tackle the task of identifying lithological and depositional facies from well logs using two distinct approaches: competitive networks and fuzzy logic. Competitive networks are a special class of neural networks that perform vector quantization of the input data by competitive learning. They are uncomplicated one-layer or two-layer networks that are small, compute-efficient, inherently well suited to classification and pattern identification, and avoid the difficulties associated with the back-propagation networks and statistical methods. This approach can be applied in two different modes, depending on the availability of core information. In the unsupervised mode, the well is segregated into distinct facies classes based solely on the internal behavior of the logs, without the use of core information. In the supervised mode, the lithological and depositional facies presented in uncored wells are identified by making use of the interdependence of observed core and log data in proximate wells that have been cored and correlating this with the behavior of the logs in the uncored wells.

Fuzzy logic represents the degree of fit of a particular observation to the definition of a set via membership functions that describe the fuzzy boundaries of that set. There are two principal advantages of this approach. First, it represents a natural way to capture and describe vagueness, uncertainty, and imperfection in the data, as fuzzy logic is intrinsically well suited to characterizing vague and imperfectly defined knowledge (a situation encountered in most geological data), and it can yield models that are simpler and more robust than those based on crisp logic. And, second, it provides a means of conveniently updating existing geological data, while fully honoring those data. In both the competitive networks and fuzzy logic approaches, quantitative confidence measures are ascribed to the results of the analysis. These measures that describe how well the procedure can identify the facies given uncertainties in the data, and both approaches can be enhanced by incorporating existing human experience and geological principles into the inference process in the form of formulated static and dynamic constraints to guide that process. Additionally, both approaches are automatic, easy to apply, robust in presence of noise, can handle data of large size and multiple log types, and do not suffer from input space distortion or non-monotonous generalization (data overfitting). The results of the two methods are in general comparable, and cross-validation tests show that their predicted facies show considerable agreement with the actual facies observed in core analysis.

The third component combines the two sources of information discussed above (seismic and well data) to extend the knowledge obtained at well locations through the use of the seismic data to attain an accurate and consistent characterization of the reservoir in the inter-well regions. There are two principal aims of this component: to estimate the point-values of the quantitative reservoir properties (such as porosity) and to provide automatic stratigraphic interpretation of the seismic data by identifying and mapping the facies present in the reservoir. To estimate the point-values of porosity from seismic data, we present an approach that utilizes regularized back propagation and radial basis neural networks. Both types of networks have inherent smoothness characteristics that alleviate the non-monotonous generalization problem associated with traditional networks and help to avert overfitting the data. The approach we present thus far has four advantages over the traditional methods: 1) it is inherently non-linear and there is no need to linearize it, so it is quite adept at capturing the intrinsic non-linearity of the problem., 2) it is virtually model-free, no a priori theoretical operator is required to link the reservoir properties to the observed seismic response, 3) a starting model is not needed, and therefore the final outcome is not dependent on the proper choice of that initial guess, and 4) it is naturally smooth, hence it has much more monotonous generalization behavior than traditional neural network methods and is not prone to overfitting. The results obtained from cross-validation tests indicate that this approach can be quite adept at estimating the porosity distribution of the reservoir, and the accuracy of the results remained consistent as the network parameters (size and training length) were varied. In contrast, the results produced by the traditional back-propagation network were inconsistent, as the traditional network gave acceptable results only when the optimal network parameters were used, and the accuracy of the network deteriorated significantly as soon as deviations from these optimal parameters occurred.

For the classification and identification of the reservoir facies from seismic data, we employ an approach based on competitive networks. As we mentioned earlier, these networks are naturally non-linear and inherently well suited to classification and pattern identification. This approach avoids many of the difficulties associated with the existing methods traditionally utilized for this task, such as multi-variant statistics, linear Bayesian inference, expert systems, and back-propagation networks (which are most suitable for point-value estimation rather than quantitative classification). Moreover, this approach can be adapted to perform either classification of the seismic facies based entirely on the characteristics of the seismic response, without requiring the use of any well information, or automatic identification and labeling of the facies where well information is available. The former is of prime use for oil prospecting in new regions, where few or no wells have been drilled, whereas the latter is most useful in development fields, where the information gained at the wells can be conveniently extended to the inter-well regions. It is especially valuable where 3D seismic surveys are available, as an areal map of the reservoir limits may be extracted from the seismic survey using this method. Cross-validation tests on synthetic and real seismic data demonstrated that the method could be an effective means of mapping the reservoir heterogeneity. For synthetic data, the output of the method showed considerable agreement with the actual geologic model used to generate the seismic data, while for the real data application, the predicted facies accurately matched those observed at the wells. Moreover, the resulting map corroborates our existing understanding of the reservoir and shows substantial similarity to the low frequency geologic model constructed by interpolating the well information, while adding significant detail and enhanced resolution to that model.

The fourth component of the approach aims to remedy the incompleteness and inconsistency of the core and well data at the early gathering and inspection stages. The accuracy of any quantitative method that subsequently attempts to extract geologic information from the data can only be as good as the accuracy of the data. We present two approaches in this thesis for accomplishing this task. To remedy the incompleteness of the data, we utilize regularized back-propagation networks to enhance wells of limited log suites by estimating the missing logs in these wells. This is achieved by analyzing the interdependence of the various log types in a well that has a complete suite of logs, and then applying the network to proximate wells whose log suites are incomplete to estimate the missing logs in those wells. To remedy the inconsistency of the data we present an approach that assigns depth corrections to core plugs by computing a coherence measure between the core and log data and maximizing that measure. This automatic correction resolves the inconsistencies between core and log information and gives rise to much better agreement between two data sets. Moreover, the resulting correction is not only automatic, and thus averts the expenditure of considerable time and effort required by the manual procedures, but it is also more accurate and less affected by subjective human performance than these procedures.